Related papers: Understanding the analysis of wave function

Fractional relaxation equations, as well as relaxation functions time-changed by independent stochastic processes have been widely studied (see, for example, \cite{MAI}, \cite{STAW} and \cite{GAR}). We start here by proving that the…

Symmetries of multi-anyon wavefunctions are analysed with the help of a second quantized formulation. Analogues of Slater determinants are constructed. It is shown that the Pauli principle is not enforced.

The behavior of monochromatic electromagnetic waves in stationary media is shown to be ruled by a frequency dependent function, which we call Wave Potential, encoded in the structure of the Helmholtz equation. Contrary to the common belief…

We study existence and stability of standing waves for coupled nonlinear Hartree type equations \[ -i\frac{\partial}{\partial t}\psi_j=\Delta \psi_j+\sum_{k=1}^m \left(W\star |\psi_k|^p \right)|\psi_j|^{p-2}\psi_j, \] where…

We calculate the correlation functions for the $\bar K^0 p, \pi^+ \Sigma^0, \pi^0 \Sigma^+, \pi^+ \Lambda$, and $\eta \Sigma^+$ states, which in the chiral unitary approach predict an excited $\Sigma^*(1/2^-)$ state at the $\bar K N$…

In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…

This work is devoted to the study of analytic wormhole solutions within the framework of $f(R)$ gravity theory. To check the possibility of having wormhole structures satisfying energy conditions, by means of the class I approach the pair…

We consider a correlated wavefunction including particle-hole pairing at half a reciprocal lattice vector for itinerant electrons hopping on a square lattice in two dimensions and subject both to on-site and nearest-neighbor repulsion. We…

Let p(t) be a trigonometric polynomial, non-negative on the unit circle. We say that a measure \sigma belongs to a polynomial Szego class, if the logarithm of its density is summable over the circle with the weight p(t). For the associated…

Given a continuous function $\phi$ defined on a domain $\Omega\subset\mathbb{R}^m\times\mathbb{R}^n$, we show that if a Pr\'ekopa-type result holds for $\phi+\psi$ for any non-negative convex function $\psi$ on $\Omega$, then $\phi$ must be…

The spectral function for an electron one-component plasma is calculated self-consistently using the GW0 approximation for the single-particle self-energy. In this way, correlation effects which go beyond the mean-field description of the…

Wave equations for some curved spacetimes may involve functions that prevent a solution in a closed form. In some cases, these functions can be eliminated by transformations and the solutions can be found analytically. In the cases where…

Since the launch of the Fermi telescope more than five years ago, many new gamma-ray pulsars have been discovered with intriguing properties challenging our current understanding of pulsar physics. Observation of the Crab pulsar furnish…

We develop the theory of generalized Weierstrass sigma- and \wp-functions defined on a trigonal curve of genus three. In particular we give a list of the associated partial differential equations satisfied by the \wp-functions, a proof that…

Following the approach of our previous paper we continue to study the asymptotic solution of periodic Schr\"{o}dinger operators. Using the eigenvalues obtained earlier the corresponding asymptotic wave functions are derived. This gives…

We present the results of energy-dependent and single-energy partial-wave analyses of pi-N elastic scattering data with laboratory kinetic energies below 2.1 GeV. We have considered the effect of adding dispersion-relation constraints…

Smooth periodic travelling waves in the Camassa--Holm (CH) equation are revisited. We show that these periodic waves can be characterized in two different ways by using two different Hamiltonian structures. The standard formulation, common…

We give a new coherent description of the first-order Fermi acceleration of particles in shock waves from the point of view of stochastic process of the individual particles, under the test particle approximation. The time development of…

We prove nonlinear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity $\psi_{tt}-\Delta \psi=\psi^p$ for $p=3,5,7,...$ in the radial case. The proof is based on a semigroup…

In the present paper, we consider the linear wave equation with the scale-invariant damping and mass. It is known that the global behavior of the solution depends on the size of the coefficients in front of the damping and mass at initial…